[Ifeffit] Re: A very quick question

[Scott Calvin]

>
>That's a very nice explanation of the utility of restraints.  I
>suspect that many out there in mailing-list-land will appreciate your
>comments quite a bit.
>
>Perhaps you could discuss more explicitly on how the error bar guides
>your choice of weight, maybe even with an example...
>
>B
>

Thanks, Bruce.

In case people aren't familiar with restraints, here's a brief 
paragraph on how they work:

Ifeffit determines the "best" fit by minimizing chi-square which is 
given by the sum of the squares of the misfits between fit and data 
at each point as scaled by an estimated error epsilon (so that the 
result is dimensionless). By default, ifeffit uses high-R noise to 
estimate epsilon, but that can be overridden (this is implemented in 
Artemis as well).  A "restraint" simply gives an expression which is 
squared and then added to chi-square, thus giving ifeffit an 
additional variable to minimize.

So one way in which I've used restraints is to fit a standard 
compound in the usual way and then move on to a related compound. The 
fit for the related compound involved more unknown parameters, and 
tended to yield high uncertainties. I expected certain values to be 
the same (or at least very close) for the sample as compared to the 
standard: S02 and E0 for example. But I was not comfortable simply 
setting the values for the sample equal to the fit from the standard, 
both because the fit has an uncertainty associated with it and 
because there could be small differences with, e.g., normalization, 
and I'd like to let ifeffit evaluate uncertainties for the sample 
parameters. So I used restraints with the uncertainty in the 
standard's parameter as the epsilon for the restraint. For example, 
in one case the fit of the standard yielded an E0 of 3.66 +/- 1.04 
eV. I therefore used the following in the sample's fit:

guess E0 = 3.66
resE0 = (E0 - 3.66)/1.04

One problem with this scheme is that it makes the estimate of epsilon 
for the data quite important. One of the beamlines I use used to have 
high-frequency oscillations in the signal which made the ifeffit 
method of estimating epsilon a poor choice. But it's probably a good 
idea to think about the epsilon generated by ifeffit anyway, and it's 
crucial to do so for multi-edge fits. In any case, it seems to me 
that the restraint method I described here maintains the proper 
statistical meaning of chi-square, with the difficulty being where it 
always was; i.e. in estimating the epsilon for the data.

--Scott Calvin
Sarah Lawrence College